LMFDB - Embedded newform 2500.1.t.a.11.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2500,1,Mod(11,2500)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2500, base_ring=CyclotomicField(250))

chi = DirichletCharacter(H, H._module([125, 238]))

N = Newforms(chi, 1, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2500.11");

S:= CuspForms(chi, 1);

N := Newforms(S);

Level:	$ N $	$=$	$ 2500 = 2^{2} \cdot 5^{4} $
Weight:	$ k $	$=$	$ 1 $
Character orbit:	$[\chi]$	$=$	2500.t (of order $250$, degree $100$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.24766253158$
Analytic rank:	$0$
Dimension:	$100$
Coefficient field:	$\Q(\zeta_{250})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{100} - x^{75} + x^{50} - x^{25} + 1 $ x^100 - x^75 + x^50 - x^25 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Projective image:	$D_{125}$
Projective field:	Galois closure of $\mathbb{Q}[x]/(x^{125} - \cdots)$

Embedding invariants

Embedding label			11.1
Root			$0.285019 - 0.958522i$ of defining polynomial
Character	$\chi$	$=$	2500.11
Dual form			2500.1.t.a.1591.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.988652 - 0.150226i) q^{2} +(0.954865 - 0.297042i) q^{4} +(0.492727 + 0.870184i) q^{5} +(0.899405 - 0.437116i) q^{8} +(0.656586 - 0.754251i) q^{9} +O(q^{10})$	\(q+(0.988652 - 0.150226i) q^{2} +(0.954865 - 0.297042i) q^{4} +(0.492727 + 0.870184i) q^{5} +(0.899405 - 0.437116i) q^{8} +(0.656586 - 0.754251i) q^{9} +(0.617860 + 0.786288i) q^{10} +(-0.268374 - 0.447357i) q^{13} +(0.823533 - 0.567269i) q^{16} +(-0.594252 + 0.839914i) q^{17} +(0.535827 - 0.844328i) q^{18} +(0.728969 + 0.684547i) q^{20} +(-0.514440 + 0.857527i) q^{25} +(-0.332533 - 0.401964i) q^{26} +(-1.52440 - 1.29370i) q^{29} +(0.728969 - 0.684547i) q^{32} +(-0.461332 + 0.919655i) q^{34} +(0.402906 - 0.915241i) q^{36} +(0.981149 + 0.751231i) q^{37} +(0.823533 + 0.567269i) q^{40} +(-1.77815 + 0.652821i) q^{41} +(0.979855 + 0.199710i) q^{45} +(-0.187381 - 0.982287i) q^{49} +(-0.379779 + 0.925077i) q^{50} +(-0.389145 - 0.347447i) q^{52} +(0.606609 + 1.59022i) q^{53} +(-1.70145 - 1.05002i) q^{58} +(-1.26792 - 0.465497i) q^{61} +(0.617860 - 0.786288i) q^{64} +(0.257047 - 0.453960i) q^{65} +(-0.317941 + 0.978522i) q^{68} +(0.260842 - 0.965382i) q^{72} +(1.78973 + 0.180532i) q^{73} +(1.08287 + 0.595312i) q^{74} +(0.899405 + 0.437116i) q^{80} +(-0.137790 - 0.990461i) q^{81} +(-1.65990 + 0.912536i) q^{82} +(-1.02368 - 0.103260i) q^{85} +(1.06153 + 0.947782i) q^{89} +(0.998737 + 0.0502443i) q^{90} +(-1.26958 + 0.783499i) q^{97} +(-0.332820 - 0.942991i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 100 q+O(q^{10}) $ 100 * q	$ 100 q+O(q^{100}) $ 100 * q

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2500\mathbb{Z}\right)^\times$.

$n$	$1251$	$1877$
$\chi(n)$	$-1$	$e\left(\frac{119}{125}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.988652	−	0.150226i	0.988652	−	0.150226i
$2$	0.988652	−	0.150226i	0.988652	−	0.150226i
$3$		0			0		0.910106	−	0.414376i	$-0.136000\pi$
$3$		0			0		−0.910106	+	0.414376i	$0.864000\pi$
$4$	0.954865	−	0.297042i	0.954865	−	0.297042i
$5$	0.492727	+	0.870184i	0.492727	+	0.870184i
$5$	0.492727	+	0.870184i	0.492727	+	0.870184i
$6$		0			0
$7$		0			0		0.637424	−	0.770513i	$-0.280000\pi$
$7$		0			0		−0.637424	+	0.770513i	$0.720000\pi$
$8$	0.899405	−	0.437116i	0.899405	−	0.437116i
$9$	0.656586	−	0.754251i	0.656586	−	0.754251i
$10$	0.617860	+	0.786288i	0.617860	+	0.786288i
$11$		0			0		−0.888136	−	0.459580i	$-0.848000\pi$
$11$		0			0		0.888136	+	0.459580i	$0.152000\pi$
$12$		0			0
$13$	−0.268374	−	0.447357i	−0.268374	−	0.447357i	0.693653	−	0.720309i	$-0.256000\pi$
$13$	−0.268374	−	0.447357i	−0.268374	−	0.447357i	−0.962028	+	0.272952i	$0.912000\pi$
$14$		0			0
$15$		0			0
$16$	0.823533	−	0.567269i	0.823533	−	0.567269i
$17$	−0.594252	+	0.839914i	−0.594252	+	0.839914i	−0.997159	−	0.0753268i	$-0.976000\pi$
$17$	−0.594252	+	0.839914i	−0.594252	+	0.839914i	0.402906	+	0.915241i	$0.368000\pi$
$18$	0.535827	−	0.844328i	0.535827	−	0.844328i
$19$		0			0		0.979855	−	0.199710i	$-0.0640000\pi$
$19$		0			0		−0.979855	+	0.199710i	$0.936000\pi$
$20$	0.728969	+	0.684547i	0.728969	+	0.684547i
$21$		0			0
$22$		0			0
$23$		0			0		−0.556876	−	0.830596i	$-0.688000\pi$
$23$		0			0		0.556876	+	0.830596i	$0.312000\pi$
$24$		0			0
$25$	−0.514440	+	0.857527i	−0.514440	+	0.857527i
$26$	−0.332533	−	0.401964i	−0.332533	−	0.401964i
$27$		0			0
$28$		0			0
$29$	−1.52440	−	1.29370i	−1.52440	−	1.29370i	−0.778462	−	0.627691i	$-0.784000\pi$
$29$	−1.52440	−	1.29370i	−1.52440	−	1.29370i	−0.745941	−	0.666012i	$-0.768000\pi$
$30$		0			0
$31$		0			0		0.577573	−	0.816339i	$-0.304000\pi$
$31$		0			0		−0.577573	+	0.816339i	$0.696000\pi$
$32$	0.728969	−	0.684547i	0.728969	−	0.684547i
$33$		0			0
$34$	−0.461332	+	0.919655i	−0.461332	+	0.919655i
$35$		0			0
$36$	0.402906	−	0.915241i	0.402906	−	0.915241i
$37$	0.981149	+	0.751231i	0.981149	+	0.751231i	0.968583	−	0.248690i	$-0.0800000\pi$
$37$	0.981149	+	0.751231i	0.981149	+	0.751231i	0.0125660	+	0.999921i	$0.496000\pi$
$38$		0			0
$39$		0			0
$40$	0.823533	+	0.567269i	0.823533	+	0.567269i
$41$	−1.77815	+	0.652821i	−1.77815	+	0.652821i	−0.778462	+	0.627691i	$0.784000\pi$
$41$	−1.77815	+	0.652821i	−1.77815	+	0.652821i	−0.999684	+	0.0251301i	$0.992000\pi$
$42$		0			0
$43$		0			0		0.425779	−	0.904827i	$-0.360000\pi$
$43$		0			0		−0.425779	+	0.904827i	$0.640000\pi$
$44$		0			0
$45$	0.979855	+	0.199710i	0.979855	+	0.199710i
$46$		0			0
$47$		0			0		−0.470704	−	0.882291i	$-0.656000\pi$
$47$		0			0		0.470704	+	0.882291i	$0.344000\pi$
$48$		0			0
$49$	−0.187381	−	0.982287i	−0.187381	−	0.982287i
$50$	−0.379779	+	0.925077i	−0.379779	+	0.925077i
$51$		0			0
$52$	−0.389145	−	0.347447i	−0.389145	−	0.347447i
$53$	0.606609	+	1.59022i	0.606609	+	1.59022i	0.793990	+	0.607930i	$0.208000\pi$
$53$	0.606609	+	1.59022i	0.606609	+	1.59022i	−0.187381	+	0.982287i	$0.560000\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$	−1.70145	−	1.05002i	−1.70145	−	1.05002i
$59$		0			0		0.212007	−	0.977268i	$-0.432000\pi$
$59$		0			0		−0.212007	+	0.977268i	$0.568000\pi$
$60$		0			0
$61$	−1.26792	−	0.465497i	−1.26792	−	0.465497i	−0.379779	−	0.925077i	$-0.624000\pi$
$61$	−1.26792	−	0.465497i	−1.26792	−	0.465497i	−0.888136	+	0.459580i	$0.848000\pi$
$62$		0			0
$63$		0			0
$64$	0.617860	−	0.786288i	0.617860	−	0.786288i
$65$	0.257047	−	0.453960i	0.257047	−	0.453960i
$66$		0			0
$67$		0			0		−0.379779	−	0.925077i	$-0.624000\pi$
$67$		0			0		0.379779	+	0.925077i	$0.376000\pi$
$68$	−0.317941	+	0.978522i	−0.317941	+	0.978522i
$69$		0			0
$70$		0			0
$71$		0			0		0.984564	−	0.175023i	$-0.0560000\pi$
$71$		0			0		−0.984564	+	0.175023i	$0.944000\pi$
$72$	0.260842	−	0.965382i	0.260842	−	0.965382i
$73$	1.78973	+	0.180532i	1.78973	+	0.180532i	0.938734	−	0.344643i	$-0.112000\pi$
$73$	1.78973	+	0.180532i	1.78973	+	0.180532i	0.850994	+	0.525175i	$0.176000\pi$
$74$	1.08287	+	0.595312i	1.08287	+	0.595312i
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		0.910106	−	0.414376i	$-0.136000\pi$
$79$		0			0		−0.910106	+	0.414376i	$0.864000\pi$
$80$	0.899405	+	0.437116i	0.899405	+	0.437116i
$81$	−0.137790	−	0.990461i	−0.137790	−	0.990461i
$82$	−1.65990	+	0.912536i	−1.65990	+	0.912536i
$83$		0			0		−0.492727	−	0.870184i	$-0.664000\pi$
$83$		0			0		0.492727	+	0.870184i	$0.336000\pi$
$84$		0			0
$85$	−1.02368	−	0.103260i	−1.02368	−	0.103260i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	1.06153	+	0.947782i	1.06153	+	0.947782i	0.998737	−	0.0502443i	$-0.0160000\pi$
$89$	1.06153	+	0.947782i	1.06153	+	0.947782i	0.0627905	+	0.998027i	$0.480000\pi$
$90$	0.998737	+	0.0502443i	0.998737	+	0.0502443i
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−1.26958	+	0.783499i	−1.26958	+	0.783499i	−0.984564	−	0.175023i	$-0.944000\pi$
$97$	−1.26958	+	0.783499i	−1.26958	+	0.783499i	−0.285019	+	0.958522i	$0.592000\pi$
$98$	−0.332820	−	0.942991i	−0.332820	−	0.942991i
$99$		0			0
$100$	−0.236499	+	0.971632i	−0.236499	+	0.971632i
$101$	−1.85016	−	0.732532i	−1.85016	−	0.732532i	−0.962028	−	0.272952i	$-0.912000\pi$
$101$	−1.85016	−	0.732532i	−1.85016	−	0.732532i	−0.888136	−	0.459580i	$-0.848000\pi$
$102$		0			0
$103$		0			0		0.954865	−	0.297042i	$-0.0960000\pi$
$103$		0			0		−0.954865	+	0.297042i	$0.904000\pi$
$104$	−0.436924	−	0.285045i	−0.436924	−	0.285045i
$105$		0			0
$106$	0.838616	+	1.48104i	0.838616	+	1.48104i
$107$		0			0		0.929776	−	0.368125i	$-0.120000\pi$
$107$		0			0		−0.929776	+	0.368125i	$0.880000\pi$
$108$		0			0
$109$	0.561240	+	1.88745i	0.561240	+	1.88745i	0.448383	+	0.893841i	$0.352000\pi$
$109$	0.561240	+	1.88745i	0.561240	+	1.88745i	0.112856	+	0.993611i	$0.464000\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.419202	−	1.93236i	0.419202	−	1.93236i	0.0627905	−	0.998027i	$-0.480000\pi$
$113$	0.419202	−	1.93236i	0.419202	−	1.93236i	0.356412	−	0.934329i	$-0.384000\pi$
$114$		0			0
$115$		0			0
$116$	−1.83988	−	0.782500i	−1.83988	−	0.782500i
$117$	−0.513630	−	0.0913066i	−0.513630	−	0.0913066i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	0.577573	+	0.816339i	0.577573	+	0.816339i
$122$	−1.32346	−	0.269741i	−1.32346	−	0.269741i
$123$		0			0
$124$		0			0
$125$	−0.999684	−	0.0251301i	−0.999684	−	0.0251301i
$126$		0			0
$127$		0			0		−0.888136	−	0.459580i	$-0.848000\pi$
$127$		0			0		0.888136	+	0.459580i	$0.152000\pi$
$128$	0.492727	−	0.870184i	0.492727	−	0.870184i
$129$		0			0
$130$	0.185934	−	0.487424i	0.185934	−	0.487424i
$131$		0			0		−0.778462	−	0.627691i	$-0.784000\pi$
$131$		0			0		0.778462	+	0.627691i	$0.216000\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	−0.167334	+	1.01518i	−0.167334	+	1.01518i
$137$	0.224573	−	0.0226529i	0.224573	−	0.0226529i	0.0125660	−	0.999921i	$-0.496000\pi$
$137$	0.224573	−	0.0226529i	0.224573	−	0.0226529i	0.212007	+	0.977268i	$0.432000\pi$
$138$		0			0
$139$		0			0		−0.656586	−	0.754251i	$-0.728000\pi$
$139$		0			0		0.656586	+	0.754251i	$0.272000\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	0.112856	−	0.993611i	0.112856	−	0.993611i
$145$	0.374644	−	1.96395i	0.374644	−	1.96395i
$146$	1.79654	−	0.0903800i	1.79654	−	0.0903800i
$147$		0			0
$148$	1.16001	+	0.425882i	1.16001	+	0.425882i
$149$	−1.06861	−	1.68386i	−1.06861	−	1.68386i	−0.597905	−	0.801567i	$-0.704000\pi$
$149$	−1.06861	−	1.68386i	−1.06861	−	1.68386i	−0.470704	−	0.882291i	$-0.656000\pi$
$150$		0			0
$151$		0			0		0.535827	−	0.844328i	$-0.320000\pi$
$151$		0			0		−0.535827	+	0.844328i	$0.680000\pi$
$152$		0			0
$153$	0.243329	+	0.999692i	0.243329	+	0.999692i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−0.889695	+	0.112395i	−0.889695	+	0.112395i	−0.556876	−	0.830596i	$-0.688000\pi$
$157$	−0.889695	+	0.112395i	−0.889695	+	0.112395i	−0.332820	+	0.942991i	$0.608000\pi$
$158$		0			0
$159$		0			0
$160$	0.954865	+	0.297042i	0.954865	+	0.297042i
$161$		0			0
$162$	−0.285019	−	0.958522i	−0.285019	−	0.958522i
$163$		0			0		0.556876	−	0.830596i	$-0.312000\pi$
$163$		0			0		−0.556876	+	0.830596i	$0.688000\pi$
$164$	−1.50397	+	1.15154i	−1.50397	+	1.15154i
$165$		0			0
$166$		0			0
$167$		0			0		0.675333	−	0.737513i	$-0.264000\pi$
$167$		0			0		−0.675333	+	0.737513i	$0.736000\pi$
$168$		0			0
$169$	0.342600	−	0.642173i	0.342600	−	0.642173i
$170$	−1.02758	+	0.0516953i	−1.02758	+	0.0516953i
$171$		0			0
$172$		0			0
$173$	−0.0707916	−	0.802697i	−0.0707916	−	0.802697i	−0.947098	−	0.320944i	$-0.896000\pi$
$173$	−0.0707916	−	0.802697i	−0.0707916	−	0.802697i	0.876307	−	0.481754i	$-0.160000\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$	1.19186	+	0.777558i	1.19186	+	0.777558i
$179$		0			0		−0.899405	−	0.437116i	$-0.856000\pi$
$179$		0			0		0.899405	+	0.437116i	$0.144000\pi$
$180$	0.994951	−	0.100362i	0.994951	−	0.100362i
$181$	−0.324350	+	0.0245019i	−0.324350	+	0.0245019i	−0.236499	−	0.971632i	$-0.576000\pi$
$181$	−0.324350	+	0.0245019i	−0.324350	+	0.0245019i	−0.0878512	+	0.996134i	$0.528000\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−0.170270	+	1.22393i	−0.170270	+	1.22393i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0		−0.402906	−	0.915241i	$-0.632000\pi$
$191$		0			0		0.402906	+	0.915241i	$0.368000\pi$
$192$		0			0
$193$	−0.562476	−	1.73112i	−0.562476	−	1.73112i	−0.675333	−	0.737513i	$-0.736000\pi$
$193$	−0.562476	−	1.73112i	−0.562476	−	1.73112i	0.112856	−	0.993611i	$-0.464000\pi$
$194$	−1.13747	+	0.965331i	−1.13747	+	0.965331i
$195$		0			0
$196$	−0.470704	−	0.882291i	−0.470704	−	0.882291i
$197$	−1.48665	+	1.19872i	−1.48665	+	1.19872i	−0.556876	+	0.830596i	$0.688000\pi$
$197$	−1.48665	+	1.19872i	−1.48665	+	1.19872i	−0.929776	+	0.368125i	$0.880000\pi$
$198$		0			0
$199$		0			0		0.728969	−	0.684547i	$-0.240000\pi$
$199$		0			0		−0.728969	+	0.684547i	$0.760000\pi$
$200$	−0.0878512	+	0.996134i	−0.0878512	+	0.996134i
$201$		0			0
$202$	−1.93921	−	0.446277i	−1.93921	−	0.446277i
$203$		0			0
$204$		0			0
$205$	−1.44422	−	1.22565i	−1.44422	−	1.22565i
$206$		0			0
$207$		0			0
$208$	−0.474787	−	0.216173i	−0.474787	−	0.216173i
$209$		0			0
$210$		0			0
$211$		0			0		0.999684	−	0.0251301i	$-0.00800000\pi$
$211$		0			0		−0.999684	+	0.0251301i	$0.992000\pi$
$212$	1.05159	+	1.33825i	1.05159	+	1.33825i
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$	0.838414	+	1.78172i	0.838414	+	1.78172i
$219$		0			0
$220$		0			0
$221$	0.535224	+	0.0404316i	0.535224	+	0.0404316i
$222$		0			0
$223$		0			0		−0.823533	−	0.567269i	$-0.808000\pi$
$223$		0			0		0.823533	+	0.567269i	$0.192000\pi$
$224$		0			0
$225$	0.309017	+	0.951057i	0.309017	+	0.951057i
$226$	0.124156	−	1.97340i	0.124156	−	1.97340i
$227$		0			0		0.617860	−	0.786288i	$-0.288000\pi$
$227$		0			0		−0.617860	+	0.786288i	$0.712000\pi$
$228$		0			0
$229$	0.591287	−	0.476768i	0.591287	−	0.476768i	−0.285019	−	0.958522i	$-0.592000\pi$
$229$	0.591287	−	0.476768i	0.591287	−	0.476768i	0.876307	+	0.481754i	$0.160000\pi$
$230$		0			0
$231$		0			0
$232$	−1.93655	−	0.497223i	−1.93655	−	0.497223i
$233$	−0.0150266	−	0.0201450i	−0.0150266	−	0.0201450i	0.793990	−	0.607930i	$-0.208000\pi$
$233$	−0.0150266	−	0.0201450i	−0.0150266	−	0.0201450i	−0.809017	+	0.587785i	$0.800000\pi$
$234$	−0.521518	−	0.0131099i	−0.521518	−	0.0131099i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		−0.448383	−	0.893841i	$-0.648000\pi$
$239$		0			0		0.448383	+	0.893841i	$0.352000\pi$
$240$		0			0
$241$	0.00662226	−	0.0750889i	0.00662226	−	0.0750889i	−0.992115	−	0.125333i	$-0.960000\pi$
$241$	0.00662226	−	0.0750889i	0.00662226	−	0.0750889i	0.998737	+	0.0502443i	$0.0160000\pi$
$242$	0.693653	+	0.720309i	0.693653	+	0.720309i
$243$		0			0
$244$	−1.34896	−	0.0678633i	−1.34896	−	0.0678633i
$245$	0.762443	−	0.647056i	0.762443	−	0.647056i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$	−0.992115	+	0.125333i	−0.992115	+	0.125333i
$251$		0			0		0.809017	−	0.587785i	$-0.200000\pi$
$251$		0			0		−0.809017	+	0.587785i	$0.800000\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	0.356412	−	0.934329i	0.356412	−	0.934329i
$257$	0.256228	+	0.101448i	0.256228	+	0.101448i	0.492727	−	0.870184i	$-0.336000\pi$
$257$	0.256228	+	0.101448i	0.256228	+	0.101448i	−0.236499	+	0.971632i	$0.576000\pi$
$258$		0			0
$259$		0			0
$260$	0.110601	−	0.509824i	0.110601	−	0.509824i
$261$	−1.97668	+	0.300356i	−1.97668	+	0.300356i
$262$		0			0
$263$		0			0		0.974527	−	0.224271i	$-0.0720000\pi$
$263$		0			0		−0.974527	+	0.224271i	$0.928000\pi$
$264$		0			0
$265$	−1.08489	+	1.31141i	−1.08489	+	1.31141i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−1.78354	−	0.812056i	−1.78354	−	0.812056i	−0.974527	−	0.224271i	$-0.928000\pi$
$269$	−1.78354	−	0.812056i	−1.78354	−	0.812056i	−0.809017	−	0.587785i	$-0.800000\pi$
$270$		0			0
$271$		0			0		−0.356412	−	0.934329i	$-0.616000\pi$
$271$		0			0		0.356412	+	0.934329i	$0.384000\pi$
$272$	−0.0129289	+	1.02880i	−0.0129289	+	1.02880i
$273$		0			0
$274$	0.218622	−	0.0561325i	0.218622	−	0.0561325i
$275$		0			0
$276$		0			0
$277$	0.665429	−	0.0167276i	0.665429	−	0.0167276i	0.309017	−	0.951057i	$-0.400000\pi$
$277$	0.665429	−	0.0167276i	0.665429	−	0.0167276i	0.356412	+	0.934329i	$0.384000\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	0.0191618	+	1.52476i	0.0191618	+	1.52476i	0.656586	+	0.754251i	$0.272000\pi$
$281$	0.0191618	+	1.52476i	0.0191618	+	1.52476i	−0.637424	+	0.770513i	$0.720000\pi$
$282$		0			0
$283$		0			0		0.356412	−	0.934329i	$-0.384000\pi$
$283$		0			0		−0.356412	+	0.934329i	$0.616000\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−0.0376902	−	0.999289i	−0.0376902	−	0.999289i
$289$	−0.0195006	−	0.0552518i	−0.0195006	−	0.0552518i
$290$	0.0753566	−	1.99795i	0.0753566	−	1.99795i
$291$		0			0
$292$	1.76257	−	0.359240i	1.76257	−	0.359240i
$293$	1.15759	+	1.08705i	1.15759	+	1.08705i	0.994951	+	0.100362i	$0.0320000\pi$
$293$	1.15759	+	1.08705i	1.15759	+	1.08705i	0.162637	+	0.986686i	$0.448000\pi$
$294$		0			0
$295$		0			0
$296$	1.21083	+	0.246785i	1.21083	+	0.246785i
$297$		0			0
$298$	−1.30944	−	1.50422i	−1.30944	−	1.50422i
$299$		0			0
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−0.219668	−	1.33268i	−0.219668	−	1.33268i
$306$	0.390747	+	0.951793i	0.390747	+	0.951793i
$307$		0			0		−0.809017	−	0.587785i	$-0.800000\pi$
$307$		0			0		0.809017	+	0.587785i	$0.200000\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.962028	−	0.272952i	$-0.0880000\pi$
$311$		0			0		−0.962028	+	0.272952i	$0.912000\pi$
$312$		0			0
$313$	1.91518	+	0.291012i	1.91518	+	0.291012i	0.994951	−	0.100362i	$-0.0320000\pi$
$313$	1.91518	+	0.291012i	1.91518	+	0.291012i	0.920232	+	0.391374i	$0.128000\pi$
$314$	−0.862714	+	0.244774i	−0.862714	+	0.244774i
$315$		0			0
$316$		0			0
$317$	−0.649264	+	0.551006i	−0.649264	+	0.551006i	−0.910106	−	0.414376i	$-0.864000\pi$
$317$	−0.649264	+	0.551006i	−0.649264	+	0.551006i	0.260842	+	0.965382i	$0.416000\pi$
$318$		0			0
$319$		0			0
$320$	0.988652	+	0.150226i	0.988652	+	0.150226i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−0.425779	−	0.904827i	−0.425779	−	0.904827i
$325$	0.521683			0.521683
$326$		0			0
$327$		0			0
$328$	−1.31392	+	1.36441i	−1.31392	+	1.36441i
$329$		0			0
$330$		0			0
$331$		0			0		−0.693653	−	0.720309i	$-0.744000\pi$
$331$		0			0		0.693653	+	0.720309i	$0.256000\pi$
$332$		0			0
$333$	1.21083	−	0.246785i	1.21083	−	0.246785i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.0141249	+	0.374496i	0.0141249	+	0.374496i	0.988652	+	0.150226i	$0.0480000\pi$
$337$	0.0141249	+	0.374496i	0.0141249	+	0.374496i	−0.974527	+	0.224271i	$0.928000\pi$
$338$	0.242242	−	0.686353i	0.242242	−	0.686353i
$339$		0			0
$340$	−1.00815	+	0.205477i	−1.00815	+	0.205477i
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$	−0.190574	−	0.782953i	−0.190574	−	0.782953i
$347$		0			0		−0.762443	−	0.647056i	$-0.776000\pi$
$347$		0			0		0.762443	+	0.647056i	$0.224000\pi$
$348$		0			0
$349$	1.81848	+	0.466907i	1.81848	+	0.466907i	0.994951	−	0.100362i	$-0.0320000\pi$
$349$	1.81848	+	0.466907i	1.81848	+	0.466907i	0.823533	+	0.567269i	$0.192000\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−0.0233672	+	1.85941i	−0.0233672	+	1.85941i	0.356412	+	0.934329i	$0.384000\pi$
$353$	−0.0233672	+	1.85941i	−0.0233672	+	1.85941i	−0.379779	+	0.925077i	$0.624000\pi$
$354$		0			0
$355$		0			0
$356$	1.29515	+	0.589686i	1.29515	+	0.589686i
$357$		0			0
$358$		0			0
$359$		0			0		0.332820	−	0.942991i	$-0.392000\pi$
$359$		0			0		−0.332820	+	0.942991i	$0.608000\pi$
$360$	0.968583	−	0.248690i	0.968583	−	0.248690i
$361$	0.920232	−	0.391374i	0.920232	−	0.391374i
$362$	−0.316989	+	0.0729495i	−0.316989	+	0.0729495i
$363$		0			0
$364$		0			0
$365$	0.724752	+	1.64635i	0.724752	+	1.64635i
$366$		0			0
$367$		0			0		−0.137790	−	0.990461i	$-0.544000\pi$
$367$		0			0		0.137790	+	0.990461i	$0.456000\pi$
$368$		0			0
$369$	−0.675114	+	1.76980i	−0.675114	+	1.76980i
$370$	0.0155281	+	1.23562i	0.0155281	+	1.23562i
$371$		0			0
$372$		0			0
$373$	−0.571620	−	1.13951i	−0.571620	−	1.13951i	−0.974527	−	0.224271i	$-0.928000\pi$
$373$	−0.571620	−	1.13951i	−0.571620	−	1.13951i	0.402906	−	0.915241i	$-0.368000\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−0.169637	+	1.02915i	−0.169637	+	1.02915i
$378$		0			0
$379$		0			0		0.597905	−	0.801567i	$-0.296000\pi$
$379$		0			0		−0.597905	+	0.801567i	$0.704000\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		−0.693653	−	0.720309i	$-0.744000\pi$
$383$		0			0		0.693653	+	0.720309i	$0.256000\pi$
$384$		0			0
$385$		0			0
$386$	−0.816152	−	1.62698i	−0.816152	−	1.62698i
$387$		0			0
$388$	−0.979549	+	1.12525i	−0.979549	+	1.12525i
$389$	−0.101481	−	1.15068i	−0.101481	−	1.15068i	−0.863923	−	0.503623i	$-0.832000\pi$
$389$	−0.101481	−	1.15068i	−0.101481	−	1.15068i	0.762443	−	0.647056i	$-0.224000\pi$
$390$		0			0
$391$		0			0
$392$	−0.597905	−	0.801567i	−0.597905	−	0.801567i
$393$		0			0
$394$	−1.28970	+	1.40845i	−1.28970	+	1.40845i
$395$		0			0
$396$		0			0
$397$	−1.04790	+	1.40484i	−1.04790	+	1.40484i	−0.137790	+	0.990461i	$0.544000\pi$
$397$	−1.04790	+	1.40484i	−1.04790	+	1.40484i	−0.910106	+	0.414376i	$0.864000\pi$
$398$		0			0
$399$		0			0
$400$	0.0627905	+	0.998027i	0.0627905	+	0.998027i
$401$	0.0618772	+	0.983510i	0.0618772	+	0.983510i	0.899405	+	0.437116i	$0.144000\pi$
$401$	0.0618772	+	0.983510i	0.0618772	+	0.983510i	−0.837528	+	0.546394i	$0.816000\pi$
$402$		0			0
$403$		0			0
$404$	−1.98425	−	0.149893i	−1.98425	−	0.149893i
$405$	0.793990	−	0.607930i	0.793990	−	0.607930i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−0.181137	−	1.09892i	−0.181137	−	1.09892i	−0.910106	−	0.414376i	$-0.864000\pi$
$409$	−0.181137	−	1.09892i	−0.181137	−	1.09892i	0.728969	−	0.684547i	$-0.240000\pi$
$410$	−1.61195	−	0.994784i	−1.61195	−	0.994784i
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$	−0.501873	−	0.142394i	−0.501873	−	0.142394i
$417$		0			0
$418$		0			0
$419$		0			0		0.899405	−	0.437116i	$-0.144000\pi$
$419$		0			0		−0.899405	+	0.437116i	$0.856000\pi$
$420$		0			0
$421$	0.0478527	+	0.421305i	0.0478527	+	0.421305i	0.994951	+	0.100362i	$0.0320000\pi$
$421$	0.0478527	+	0.421305i	0.0478527	+	0.421305i	−0.947098	+	0.320944i	$0.896000\pi$
$422$		0			0
$423$		0			0
$424$	1.24070	+	1.16509i	1.24070	+	1.16509i
$425$	−0.414542	−	0.941672i	−0.414542	−	0.941672i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		0.762443	−	0.647056i	$-0.224000\pi$
$431$		0			0		−0.762443	+	0.647056i	$0.776000\pi$
$432$		0			0
$433$	0.282808	−	1.16189i	0.282808	−	1.16189i	−0.637424	−	0.770513i	$-0.720000\pi$
$433$	0.282808	−	1.16189i	0.282808	−	1.16189i	0.920232	−	0.391374i	$-0.128000\pi$
$434$		0			0
$435$		0			0
$436$	1.09656	+	1.63555i	1.09656	+	1.63555i
$437$		0			0
$438$		0			0
$439$		0			0		0.0376902	−	0.999289i	$-0.488000\pi$
$439$		0			0		−0.0376902	+	0.999289i	$0.512000\pi$
$440$		0			0
$441$	−0.863923	−	0.503623i	−0.863923	−	0.503623i
$442$	0.535224	−	0.0404316i	0.535224	−	0.0404316i
$443$		0			0		1.00000			$0$
$443$		0			0		−1.00000			$\pi$
$444$		0			0
$445$	−0.301701	+	1.39072i	−0.301701	+	1.39072i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	1.76227	−	0.222626i	1.76227	−	0.222626i	0.823533	−	0.567269i	$-0.192000\pi$
$449$	1.76227	−	0.222626i	1.76227	−	0.222626i	0.938734	+	0.344643i	$0.112000\pi$
$450$	0.448383	+	0.893841i	0.448383	+	0.893841i
$451$		0			0
$452$	−0.173708	−	1.96966i	−0.173708	−	1.96966i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−0.273190	−	1.43211i	−0.273190	−	1.43211i	−0.809017	−	0.587785i	$-0.800000\pi$
$457$	−0.273190	−	1.43211i	−0.273190	−	1.43211i	0.535827	−	0.844328i	$-0.320000\pi$
$458$	0.512955	−	0.560184i	0.512955	−	0.560184i
$459$		0			0
$460$		0			0
$461$	−0.139506	+	0.106815i	−0.139506	+	0.106815i	−0.675333	−	0.737513i	$-0.736000\pi$
$461$	−0.139506	+	0.106815i	−0.139506	+	0.106815i	0.535827	+	0.844328i	$0.320000\pi$
$462$		0			0
$463$		0			0		−0.285019	−	0.958522i	$-0.592000\pi$
$463$		0			0		0.285019	+	0.958522i	$0.408000\pi$
$464$	−1.98927	−	0.200660i	−1.98927	−	0.200660i
$465$		0			0
$466$	−0.0178824	−	0.0176591i	−0.0178824	−	0.0176591i
$467$		0			0		0.837528	−	0.546394i	$-0.184000\pi$
$467$		0			0		−0.837528	+	0.546394i	$0.816000\pi$
$468$	−0.517569	+	0.0653842i	−0.517569	+	0.0653842i
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$	1.59771	+	0.586578i	1.59771	+	0.586578i
$478$		0			0
$479$		0			0		0.998737	−	0.0502443i	$-0.0160000\pi$
$479$		0			0		−0.998737	+	0.0502443i	$0.984000\pi$
$480$		0			0
$481$	0.0727533	−	0.640535i	0.0727533	−	0.640535i
$482$	−0.00473317	−	0.0752316i	−0.00473317	−	0.0752316i
$483$		0			0
$484$	0.793990	+	0.607930i	0.793990	+	0.607930i
$485$	−1.30735	−	0.718720i	−1.30735	−	0.718720i
$486$		0			0
$487$		0			0		−0.920232	−	0.391374i	$-0.872000\pi$
$487$		0			0		0.920232	+	0.391374i	$0.128000\pi$
$488$	−1.34385	+	0.135555i	−1.34385	+	0.135555i
$489$		0			0
$490$	0.656586	−	0.754251i	0.656586	−	0.754251i
$491$		0			0		−0.514440	−	0.857527i	$-0.672000\pi$
$491$		0			0		0.514440	+	0.857527i	$0.328000\pi$
$492$		0			0
$493$	1.99248	−	0.511582i	1.99248	−	0.511582i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$499$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$500$	−0.962028	+	0.272952i	−0.962028	+	0.272952i
$501$		0			0
$502$		0			0
$503$		0			0		−0.979855	−	0.199710i	$-0.936000\pi$
$503$		0			0		0.979855	+	0.199710i	$0.0640000\pi$
$504$		0			0
$505$	−0.274189	−	1.97092i	−0.274189	−	1.97092i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	1.20842	+	0.513941i	1.20842	+	0.513941i	0.899405	−	0.437116i	$-0.144000\pi$
$509$	1.20842	+	0.513941i	1.20842	+	0.513941i	0.309017	+	0.951057i	$0.400000\pi$
$510$		0			0
$511$		0			0
$512$	0.212007	−	0.977268i	0.212007	−	0.977268i
$513$		0			0
$514$	0.268561	+	0.0618047i	0.268561	+	0.0618047i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	0.0327567	−	0.520654i	0.0327567	−	0.520654i
$521$	0.396149	+	0.258443i	0.396149	+	0.258443i	0.728969	−	0.684547i	$-0.240000\pi$
$521$	0.396149	+	0.258443i	0.396149	+	0.258443i	−0.332820	+	0.942991i	$0.608000\pi$
$522$	−1.90913	+	0.593896i	−1.90913	+	0.593896i
$523$		0			0		0.0376902	−	0.999289i	$-0.488000\pi$
$523$		0			0		−0.0376902	+	0.999289i	$0.512000\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	−0.379779	+	0.925077i	−0.379779	+	0.925077i
$530$	−0.875570	+	1.45950i	−0.875570	+	1.45950i
$531$		0			0
$532$		0			0
$533$	0.769253	+	0.620266i	0.769253	+	0.620266i
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	−1.88530	−	0.534907i	−1.88530	−	0.534907i
$539$		0			0
$540$		0			0
$541$	−0.0620782	−	1.64589i	−0.0620782	−	1.64589i	−0.597905	−	0.801567i	$-0.704000\pi$
$541$	−0.0620782	−	1.64589i	−0.0620782	−	1.64589i	0.535827	−	0.844328i	$-0.320000\pi$
$542$		0			0
$543$		0			0
$544$	0.141770	+	1.01907i	0.141770	+	1.01907i
$545$	−1.36589	+	1.41838i	−1.36589	+	1.41838i
$546$		0			0
$547$		0			0		−0.899405	−	0.437116i	$-0.856000\pi$
$547$		0			0		0.899405	+	0.437116i	$0.144000\pi$
$548$	0.207708	−	0.0883380i	0.207708	−	0.0883380i
$549$	−1.18360	+	0.650688i	−1.18360	+	0.650688i
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$	0.655365	−	0.116502i	0.655365	−	0.116502i
$555$		0			0
$556$		0			0
$557$	−0.548899	+	1.68934i	−0.548899	+	1.68934i	0.162637	+	0.986686i	$0.448000\pi$
$557$	−0.548899	+	1.68934i	−0.548899	+	1.68934i	−0.711536	+	0.702650i	$0.752000\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	0.248003	+	1.50458i	0.248003	+	1.50458i
$563$		0			0		0.448383	−	0.893841i	$-0.352000\pi$
$563$		0			0		−0.448383	+	0.893841i	$0.648000\pi$
$564$		0			0
$565$	1.88806	−	0.587341i	1.88806	−	0.587341i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	0.460949	−	1.89376i	0.460949	−	1.89376i	0.0125660	−	0.999921i	$-0.496000\pi$
$569$	0.460949	−	1.89376i	0.460949	−	1.89376i	0.448383	−	0.893841i	$-0.352000\pi$
$570$		0			0
$571$		0			0		0.137790	−	0.990461i	$-0.456000\pi$
$571$		0			0		−0.137790	+	0.990461i	$0.544000\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	−0.187381	−	0.982287i	−0.187381	−	0.982287i
$577$	1.02077	−	1.70153i	1.02077	−	1.70153i	0.402906	−	0.915241i	$-0.368000\pi$
$577$	1.02077	−	1.70153i	1.02077	−	1.70153i	0.617860	−	0.786288i	$-0.288000\pi$
$578$	−0.0275795	−	0.0516953i	−0.0275795	−	0.0516953i
$579$		0			0
$580$	−0.225641	−	1.98660i	−0.225641	−	1.98660i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	1.68860	−	0.619947i	1.68860	−	0.619947i
$585$	−0.173626	−	0.491942i	−0.173626	−	0.491942i
$586$	1.30775	+	0.900812i	1.30775	+	0.900812i
$587$		0			0		0.938734	−	0.344643i	$-0.112000\pi$
$587$		0			0		−0.938734	+	0.344643i	$0.888000\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	1.23416	+	0.0620879i	1.23416	+	0.0620879i
$593$	1.20066	−	1.12749i	1.20066	−	1.12749i	0.212007	−	0.977268i	$-0.432000\pi$
$593$	1.20066	−	1.12749i	1.20066	−	1.12749i	0.988652	−	0.150226i	$-0.0480000\pi$
$594$		0			0
$595$		0			0
$596$	−1.52055	−	1.29044i	−1.52055	−	1.29044i
$597$		0			0
$598$		0			0
$599$		0			0		−0.637424	−	0.770513i	$-0.720000\pi$
$599$		0			0		0.637424	+	0.770513i	$0.280000\pi$
$600$		0			0
$601$	1.06772	−	1.29065i	1.06772	−	1.29065i	0.112856	−	0.993611i	$-0.464000\pi$
$601$	1.06772	−	1.29065i	1.06772	−	1.29065i	0.954865	−	0.297042i	$-0.0960000\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−0.425779	+	0.904827i	−0.425779	+	0.904827i
$606$		0			0
$607$		0			0		0.535827	−	0.844328i	$-0.320000\pi$
$607$		0			0		−0.535827	+	0.844328i	$0.680000\pi$
$608$		0			0
$609$		0			0
$610$	−0.417379	−	1.28456i	−0.417379	−	1.28456i
$611$		0			0
$612$	0.529296	+	0.882291i	0.529296	+	0.882291i
$613$	−1.40048	+	1.25042i	−1.40048	+	1.25042i	−0.470704	+	0.882291i	$0.656000\pi$
$613$	−1.40048	+	1.25042i	−1.40048	+	1.25042i	−0.929776	+	0.368125i	$0.880000\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.03894	−	0.504932i	1.03894	−	0.504932i	0.162637	−	0.986686i	$-0.448000\pi$
$617$	1.03894	−	0.504932i	1.03894	−	0.504932i	0.876307	+	0.481754i	$0.160000\pi$
$618$		0			0
$619$		0			0		0.837528	−	0.546394i	$-0.184000\pi$
$619$		0			0		−0.837528	+	0.546394i	$0.816000\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−0.470704	−	0.882291i	−0.470704	−	0.882291i
$626$	1.93717			1.93717
$627$		0			0
$628$	−0.816152	+	0.371598i	−0.816152	+	0.371598i
$629$	−1.21402	+	0.377660i	−1.21402	+	0.377660i
$630$		0			0
$631$		0			0		0.837528	−	0.546394i	$-0.184000\pi$
$631$		0			0		−0.837528	+	0.546394i	$0.816000\pi$
$632$		0			0
$633$		0			0
$634$	−0.559121	+	0.642289i	−0.559121	+	0.642289i
$635$		0			0
$636$		0			0
$637$	−0.389145	+	0.347447i	−0.389145	+	0.347447i
$638$		0			0
$639$		0			0
$640$	1.00000			1.00000
$641$	0.103420	−	0.0712382i	0.103420	−	0.0712382i	−0.514440	−	0.857527i	$-0.672000\pi$
$641$	0.103420	−	0.0712382i	0.103420	−	0.0712382i	0.617860	+	0.786288i	$0.288000\pi$
$642$		0			0
$643$		0			0		0.535827	−	0.844328i	$-0.320000\pi$
$643$		0			0		−0.535827	+	0.844328i	$0.680000\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		−0.947098	−	0.320944i	$-0.896000\pi$
$647$		0			0		0.947098	+	0.320944i	$0.104000\pi$
$648$	−0.556876	−	0.830596i	−0.556876	−	0.830596i
$649$		0			0
$650$	0.515763	−	0.0783701i	0.515763	−	0.0783701i
$651$		0			0
$652$		0			0
$653$	−0.161032	+	0.392246i	−0.161032	+	0.392246i	−0.984564	−	0.175023i	$-0.944000\pi$
$653$	−0.161032	+	0.392246i	−0.161032	+	0.392246i	0.823533	+	0.567269i	$0.192000\pi$
$654$		0			0
$655$		0			0
$656$	−1.09404	+	1.54631i	−1.09404	+	1.54631i
$657$	1.31128	−	1.23137i	1.31128	−	1.23137i
$658$		0			0
$659$		0			0		0.448383	−	0.893841i	$-0.352000\pi$
$659$		0			0		−0.448383	+	0.893841i	$0.648000\pi$
$660$		0			0
$661$	0.431776	−	0.980821i	0.431776	−	0.980821i	−0.556876	−	0.830596i	$-0.688000\pi$
$661$	0.431776	−	0.980821i	0.431776	−	0.980821i	0.988652	−	0.150226i	$-0.0480000\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$	1.16001	−	0.425882i	1.16001	−	0.425882i
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−0.847315	+	1.41240i	−0.847315	+	1.41240i	0.0627905	+	0.998027i	$0.480000\pi$
$673$	−0.847315	+	1.41240i	−0.847315	+	1.41240i	−0.910106	+	0.414376i	$0.864000\pi$
$674$	0.0702235	+	0.368125i	0.0702235	+	0.368125i
$675$		0			0
$676$	0.136385	−	0.714955i	0.136385	−	0.714955i
$677$	1.48012	+	1.32152i	1.48012	+	1.32152i	0.823533	+	0.567269i	$0.192000\pi$
$677$	1.48012	+	1.32152i	1.48012	+	1.32152i	0.656586	+	0.754251i	$0.272000\pi$
$678$		0			0
$679$		0			0
$680$	−0.965844	+	0.354596i	−0.965844	+	0.354596i
$681$		0			0
$682$		0			0
$683$		0			0		−0.850994	−	0.525175i	$-0.824000\pi$
$683$		0			0		0.850994	+	0.525175i	$0.176000\pi$
$684$		0			0
$685$	0.130366	+	0.184258i	0.130366	+	0.184258i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	0.548597	−	0.698145i	0.548597	−	0.698145i
$690$		0			0
$691$		0			0		0.994951	−	0.100362i	$-0.0320000\pi$
$691$		0			0		−0.994951	+	0.100362i	$0.968000\pi$
$692$	−0.306031	−	0.745439i	−0.306031	−	0.745439i
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$	0.508354	−	1.88143i	0.508354	−	1.88143i
$698$	1.86799	+	0.188426i	1.86799	+	0.188426i
$699$		0			0
$700$		0			0
$701$	1.75040	−	0.962290i	1.75040	−	0.962290i	0.850994	−	0.525175i	$-0.176000\pi$
$701$	1.75040	−	0.962290i	1.75040	−	0.962290i	0.899405	−	0.437116i	$-0.144000\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	0.256228	+	1.84182i	0.256228	+	1.84182i
$707$		0			0
$708$		0			0
$709$	0.0586808	+	1.55582i	0.0586808	+	1.55582i	0.656586	+	0.754251i	$0.272000\pi$
$709$	0.0586808	+	1.55582i	0.0586808	+	1.55582i	−0.597905	+	0.801567i	$0.704000\pi$
$710$		0			0
$711$		0			0
$712$	1.36903	+	0.388430i	1.36903	+	0.388430i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		−0.597905	−	0.801567i	$-0.704000\pi$
$719$		0			0		0.597905	+	0.801567i	$0.296000\pi$
$720$	0.920232	−	0.391374i	0.920232	−	0.391374i
$721$		0			0
$722$	0.850994	−	0.525175i	0.850994	−	0.525175i
$723$		0			0
$724$	−0.302432	+	0.119741i	−0.302432	+	0.119741i
$725$	1.89360	−	0.641685i	1.89360	−	0.641685i
$726$		0			0
$727$		0			0		0.0376902	−	0.999289i	$-0.488000\pi$
$727$		0			0		−0.0376902	+	0.999289i	$0.512000\pi$
$728$		0			0
$729$	−0.837528	−	0.546394i	−0.837528	−	0.546394i
$730$	0.963851	+	1.51879i	0.963851	+	1.51879i
$731$		0			0
$732$		0			0
$733$	0.00157806	+	0.125571i	0.00157806	+	0.125571i	0.998737	+	0.0502443i	$0.0160000\pi$
$733$	0.00157806	+	0.125571i	0.00157806	+	0.125571i	−0.997159	+	0.0753268i	$0.976000\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$	−0.401583	+	1.85114i	−0.401583	+	1.85114i
$739$		0			0		0.711536	−	0.702650i	$-0.248000\pi$
$739$		0			0		−0.711536	+	0.702650i	$0.752000\pi$
$740$	0.200974	+	1.21927i	0.200974	+	1.21927i
$741$		0			0
$742$		0			0
$743$		0			0		0.0627905	−	0.998027i	$-0.480000\pi$
$743$		0			0		−0.0627905	+	0.998027i	$0.520000\pi$
$744$		0			0
$745$	0.938733	−	1.75957i	0.938733	−	1.75957i
$746$	−0.736317	−	1.04071i	−0.736317	−	1.04071i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		−0.309017	−	0.951057i	$-0.600000\pi$
$751$		0			0		0.309017	+	0.951057i	$0.400000\pi$
$752$		0			0
$753$		0			0
$754$	−0.0131068	+	1.04295i	−0.0131068	+	1.04295i
$755$		0			0
$756$		0			0
$757$	1.89814	−	0.487360i	1.89814	−	0.487360i	0.899405	−	0.437116i	$-0.144000\pi$
$757$	1.89814	−	0.487360i	1.89814	−	0.487360i	0.998737	−	0.0502443i	$-0.0160000\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−0.0448196	+	0.271911i	−0.0448196	+	0.271911i	−0.999684	−	0.0251301i	$-0.992000\pi$
$761$	−0.0448196	+	0.271911i	−0.0448196	+	0.271911i	0.954865	+	0.297042i	$0.0960000\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−0.750021	+	0.704316i	−0.750021	+	0.704316i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	0.197794	−	1.74142i	0.197794	−	1.74142i	−0.379779	−	0.925077i	$-0.624000\pi$
$769$	0.197794	−	1.74142i	0.197794	−	1.74142i	0.577573	−	0.816339i	$-0.304000\pi$
$770$		0			0
$771$		0			0
$772$	−1.05130	−	1.48591i	−1.05130	−	1.48591i
$773$	−0.883731	−	0.324450i	−0.883731	−	0.324450i	−0.137790	−	0.990461i	$-0.544000\pi$
$773$	−0.883731	−	0.324450i	−0.883731	−	0.324450i	−0.745941	+	0.666012i	$0.768000\pi$
$774$		0			0
$775$		0			0
$776$	−0.799391	+	1.25964i	−0.799391	+	1.25964i
$777$		0			0
$778$	−0.273191	−	1.12238i	−0.273191	−	1.12238i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−0.711536	−	0.702650i	−0.711536	−	0.702650i
$785$	−0.536181	−	0.718818i	−0.536181	−	0.718818i
$786$		0			0
$787$		0			0		−0.285019	−	0.958522i	$-0.592000\pi$
$787$		0			0		0.285019	+	0.958522i	$0.408000\pi$
$788$	−1.06348	+	1.58621i	−1.06348	+	1.58621i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	0.132032	+	0.692139i	0.132032	+	0.692139i
$794$	−0.824962	+	1.54632i	−0.824962	+	1.54632i
$795$		0			0
$796$		0			0
$797$	−0.159168	+	1.14413i	−0.159168	+	1.14413i	0.728969	+	0.684547i	$0.240000\pi$
$797$	−0.159168	+	1.14413i	−0.159168	+	1.14413i	−0.888136	+	0.459580i	$0.848000\pi$
$798$		0			0
$799$		0			0
$800$	0.212007	+	0.977268i	0.212007	+	0.977268i
$801$	1.41185	−	0.178358i	1.41185	−	0.178358i
$802$	0.208923	+	0.963053i	0.208923	+	0.963053i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	−1.98425	+	0.149893i	−1.98425	+	0.149893i
$809$	1.68383	+	0.981589i	1.68383	+	0.981589i	0.954865	+	0.297042i	$0.0960000\pi$
$809$	1.68383	+	0.981589i	1.68383	+	0.981589i	0.728969	+	0.684547i	$0.240000\pi$
$810$	0.693653	−	0.720309i	0.693653	−	0.720309i
$811$		0			0		0.0376902	−	0.999289i	$-0.488000\pi$
$811$		0			0		−0.0376902	+	0.999289i	$0.512000\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	−0.344168	−	1.05924i	−0.344168	−	1.05924i
$819$		0			0
$820$	−1.74310	−	0.741339i	−1.74310	−	0.741339i
$821$	0.600076	+	1.12479i	0.600076	+	1.12479i	0.979855	+	0.199710i	$0.0640000\pi$
$821$	0.600076	+	1.12479i	0.600076	+	1.12479i	−0.379779	+	0.925077i	$0.624000\pi$
$822$		0			0
$823$		0			0		0.863923	−	0.503623i	$-0.168000\pi$
$823$		0			0		−0.863923	+	0.503623i	$0.832000\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		−0.974527	−	0.224271i	$-0.928000\pi$
$827$		0			0		0.974527	+	0.224271i	$0.0720000\pi$
$828$		0			0
$829$	−0.175709	−	1.54698i	−0.175709	−	1.54698i	−0.711536	−	0.702650i	$-0.752000\pi$
$829$	−0.175709	−	1.54698i	−0.175709	−	1.54698i	0.535827	−	0.844328i	$-0.320000\pi$
$830$		0			0
$831$		0			0
$832$	−0.517569	−	0.0653842i	−0.517569	−	0.0653842i
$833$	0.936389	+	0.426342i	0.936389	+	0.426342i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		0.863923	−	0.503623i	$-0.168000\pi$
$839$		0			0		−0.863923	+	0.503623i	$0.832000\pi$
$840$		0			0
$841$	0.487501	+	2.95757i	0.487501	+	2.95757i
$842$	0.110601	+	0.409336i	0.110601	+	0.409336i
$843$		0			0
$844$		0			0
$845$	0.727617	−	0.0182909i	0.727617	−	0.0182909i
$846$		0			0
$847$		0			0
$848$	1.40164	+	0.965485i	1.40164	+	0.965485i
$849$		0			0
$850$	−0.551301	−	0.868711i	−0.551301	−	0.868711i
$851$		0			0
$852$		0			0
$853$	0.454144	−	0.608837i	0.454144	−	0.608837i	−0.514440	−	0.857527i	$-0.672000\pi$
$853$	0.454144	−	0.608837i	0.454144	−	0.608837i	0.968583	+	0.248690i	$0.0800000\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	1.41213	+	0.362574i	1.41213	+	0.362574i	0.876307	−	0.481754i	$-0.160000\pi$
$857$	1.41213	+	0.362574i	1.41213	+	0.362574i	0.535827	+	0.844328i	$0.320000\pi$
$858$		0			0
$859$		0			0		−0.999684	−	0.0251301i	$-0.992000\pi$
$859$		0			0		0.999684	+	0.0251301i	$0.00800000\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.402906	−	0.915241i	$-0.632000\pi$
$863$		0			0		0.402906	+	0.915241i	$0.368000\pi$
$864$		0			0
$865$	0.663613	−	0.457113i	0.663613	−	0.457113i
$866$	0.105053	−	1.19119i	0.105053	−	1.19119i
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	1.32982	+	1.45226i	1.32982	+	1.45226i
$873$	−0.242636	+	1.47202i	−0.242636	+	1.47202i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−0.422111	−	0.841469i	−0.422111	−	0.841469i	−0.999684	−	0.0251301i	$-0.992000\pi$
$877$	−0.422111	−	0.841469i	−0.422111	−	0.841469i	0.577573	−	0.816339i	$-0.304000\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−0.662767	+	1.73743i	−0.662767	+	1.73743i	0.0125660	+	0.999921i	$0.496000\pi$
$881$	−0.662767	+	1.73743i	−0.662767	+	1.73743i	−0.675333	+	0.737513i	$0.736000\pi$
$882$	−0.929776	−	0.368125i	−0.929776	−	0.368125i
$883$		0			0		−0.137790	−	0.990461i	$-0.544000\pi$
$883$		0			0		0.137790	+	0.990461i	$0.456000\pi$
$884$	0.523076	−	0.120377i	0.523076	−	0.120377i
$885$		0			0
$886$		0			0
$887$		0			0		−0.863923	−	0.503623i	$-0.832000\pi$
$887$		0			0		0.863923	+	0.503623i	$0.168000\pi$
$888$		0			0
$889$		0			0
$890$	−0.0893554	+	1.42026i	−0.0893554	+	1.42026i
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	1.70882	−	0.484837i	1.70882	−	0.484837i
$899$		0			0
$900$	0.577573	+	0.816339i	0.577573	+	0.816339i
$901$	−1.69613	−	0.435491i	−1.69613	−	0.435491i
$902$		0			0
$903$		0			0
$904$	−0.467630	−	1.92121i	−0.467630	−	1.92121i
$905$	−0.181137	−	0.270172i	−0.181137	−	0.270172i
$906$		0			0
$907$		0			0		−0.876307	−	0.481754i	$-0.840000\pi$
$907$		0			0		0.876307	+	0.481754i	$0.160000\pi$
$908$		0			0
$909$	−1.76730	+	0.914519i	−1.76730	+	0.914519i
$910$		0			0
$911$		0			0		−0.212007	−	0.977268i	$-0.568000\pi$
$911$		0			0		0.212007	+	0.977268i	$0.432000\pi$
$912$		0			0
$913$		0			0
$914$	−0.485230	−	1.37482i	−0.485230	−	1.37482i
$915$		0			0
$916$	0.422979	−	0.630886i	0.422979	−	0.630886i
$917$		0			0
$918$		0			0
$919$		0			0		−0.693653	−	0.720309i	$-0.744000\pi$
$919$		0			0		0.693653	+	0.720309i	$0.256000\pi$
$920$		0			0
$921$		0			0
$922$	−0.121877	+	0.126560i	−0.121877	+	0.126560i
$923$		0			0
$924$		0			0
$925$	−1.14894	+	0.454899i	−1.14894	+	0.454899i
$926$		0			0
$927$		0			0
$928$	−1.99684	+	0.100457i	−1.99684	+	0.100457i
$929$	0.294119	−	0.305421i	0.294119	−	0.305421i	−0.556876	−	0.830596i	$-0.688000\pi$
$929$	0.294119	−	0.305421i	0.294119	−	0.305421i	0.850994	+	0.525175i	$0.176000\pi$
$930$		0			0
$931$		0			0
$932$	−0.0203323	−	0.0147723i	−0.0203323	−	0.0147723i
$933$		0			0
$934$		0			0
$935$		0			0
$936$	−0.501873	+	0.142394i	−0.501873	+	0.142394i
$937$	−0.0745249	−	0.0113241i	−0.0745249	−	0.0113241i	0.112856	−	0.993611i	$-0.464000\pi$
$937$	−0.0745249	−	0.0113241i	−0.0745249	−	0.0113241i	−0.187381	+	0.982287i	$0.560000\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−1.18454	+	1.05761i	−1.18454	+	1.05761i	−0.187381	+	0.982287i	$0.560000\pi$
$941$	−1.18454	+	1.05761i	−1.18454	+	1.05761i	−0.997159	+	0.0753268i	$0.976000\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		0.998737	−	0.0502443i	$-0.0160000\pi$
$947$		0			0		−0.998737	+	0.0502443i	$0.984000\pi$
$948$		0			0
$949$	−0.399555	−	0.849098i	−0.399555	−	0.849098i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−1.35197	+	1.40392i	−1.35197	+	1.40392i	−0.514440	+	0.857527i	$0.672000\pi$
$953$	−1.35197	+	1.40392i	−1.35197	+	1.40392i	−0.837528	+	0.546394i	$0.816000\pi$
$954$	1.66770	+	0.339904i	1.66770	+	0.339904i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−0.332820	−	0.942991i	−0.332820	−	0.942991i
$962$	−0.0242971	−	0.644196i	−0.0242971	−	0.644196i
$963$		0			0
$964$	−0.0159812	−	0.0736668i	−0.0159812	−	0.0736668i
$965$	1.22925	−	1.34243i	1.22925	−	1.34243i
$966$		0			0
$967$		0			0		0.356412	−	0.934329i	$-0.384000\pi$
$967$		0			0		−0.356412	+	0.934329i	$0.616000\pi$
$968$	0.876307	+	0.481754i	0.876307	+	0.481754i
$969$		0			0
$970$	−1.40048	−	0.514167i	−1.40048	−	0.514167i
$971$		0			0		−0.236499	−	0.971632i	$-0.576000\pi$
$971$		0			0		0.236499	+	0.971632i	$0.424000\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$	−1.30823	+	0.335897i	−1.30823	+	0.335897i
$977$	−1.33463	+	0.378668i	−1.33463	+	0.378668i	−0.863923	−	0.503623i	$-0.832000\pi$
$977$	−1.33463	+	0.378668i	−1.33463	+	0.378668i	−0.470704	+	0.882291i	$0.656000\pi$
$978$		0			0
$979$		0			0
$980$	0.535827	−	0.844328i	0.535827	−	0.844328i
$981$	1.79212	+	0.815959i	1.79212	+	0.815959i
$982$		0			0
$983$		0			0		−0.954865	−	0.297042i	$-0.904000\pi$
$983$		0			0		0.954865	+	0.297042i	$0.0960000\pi$
$984$		0			0
$985$	−1.77562	−	0.703018i	−1.77562	−	0.703018i
$986$	1.89302	−	0.805098i	1.89302	−	0.805098i
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		0.974527	−	0.224271i	$-0.0720000\pi$
$991$		0			0		−0.974527	+	0.224271i	$0.928000\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	0.197794	+	1.74142i	0.197794	+	1.74142i	0.577573	+	0.816339i	$0.304000\pi$
$997$	0.197794	+	1.74142i	0.197794	+	1.74142i	−0.379779	+	0.925077i	$0.624000\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2500.1.t.a.11.1	✓	100
4.3	odd	2	CM	2500.1.t.a.11.1	✓	100
625.341	even	125	inner	2500.1.t.a.1591.1	yes	100
2500.1591	odd	250	inner	2500.1.t.a.1591.1	yes	100

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2500.1.t.a.11.1	✓	100	1.1	even	1	trivial
2500.1.t.a.11.1	✓	100	4.3	odd	2	CM
2500.1.t.a.1591.1	yes	100	625.341	even	125	inner
2500.1.t.a.1591.1	yes	100	2500.1591	odd	250	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2500 = 2^{2} \cdot 5^{4} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	2500.t (of order \(250\), degree \(100\), minimal)

\(f(q)\)	\(=\)	\(q+(0.988652 - 0.150226i) q^{2} +(0.954865 - 0.297042i) q^{4} +(0.492727 + 0.870184i) q^{5} +(0.899405 - 0.437116i) q^{8} +(0.656586 - 0.754251i) q^{9} +O(q^{10})\)	\(q+(0.988652 - 0.150226i) q^{2} +(0.954865 - 0.297042i) q^{4} +(0.492727 + 0.870184i) q^{5} +(0.899405 - 0.437116i) q^{8} +(0.656586 - 0.754251i) q^{9} +(0.617860 + 0.786288i) q^{10} +(-0.268374 - 0.447357i) q^{13} +(0.823533 - 0.567269i) q^{16} +(-0.594252 + 0.839914i) q^{17} +(0.535827 - 0.844328i) q^{18} +(0.728969 + 0.684547i) q^{20} +(-0.514440 + 0.857527i) q^{25} +(-0.332533 - 0.401964i) q^{26} +(-1.52440 - 1.29370i) q^{29} +(0.728969 - 0.684547i) q^{32} +(-0.461332 + 0.919655i) q^{34} +(0.402906 - 0.915241i) q^{36} +(0.981149 + 0.751231i) q^{37} +(0.823533 + 0.567269i) q^{40} +(-1.77815 + 0.652821i) q^{41} +(0.979855 + 0.199710i) q^{45} +(-0.187381 - 0.982287i) q^{49} +(-0.379779 + 0.925077i) q^{50} +(-0.389145 - 0.347447i) q^{52} +(0.606609 + 1.59022i) q^{53} +(-1.70145 - 1.05002i) q^{58} +(-1.26792 - 0.465497i) q^{61} +(0.617860 - 0.786288i) q^{64} +(0.257047 - 0.453960i) q^{65} +(-0.317941 + 0.978522i) q^{68} +(0.260842 - 0.965382i) q^{72} +(1.78973 + 0.180532i) q^{73} +(1.08287 + 0.595312i) q^{74} +(0.899405 + 0.437116i) q^{80} +(-0.137790 - 0.990461i) q^{81} +(-1.65990 + 0.912536i) q^{82} +(-1.02368 - 0.103260i) q^{85} +(1.06153 + 0.947782i) q^{89} +(0.998737 + 0.0502443i) q^{90} +(-1.26958 + 0.783499i) q^{97} +(-0.332820 - 0.942991i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 100 q+O(q^{10}) \) 100 * q	\( 100 q+O(q^{100}) \) 100 * q

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more